Question of the Day - 04 June 2020

What are the chances of going 0 for 10 on an open-ended flush or straight draw? (This would not be necessarily unique to Ultimate X, of course.) I thought that for the flush, it would be 0.8 to the tenth power (rounding, obviously). That number is roughly 0.1--does that mean that an 0 for 10 would happen once in every ten trials?

Not just for you Kevin but for every reader.  The key word in Dancers "explanation" is chances.  Mathematically speaking he is attempting to use Probability math to determine the outcome of a chance, the only problem with such an attempt is that it eliminates maths chaos theory in such calculations.  In other words you have an equal chance to get zero results as you would all 10 draws filling as an open ended straight or flush. The only difference in the Ultimate version is the random multipliers for each hand which of course vary the payout.

I know Bob Dancer doesn't need me to defend his numbers, in fact he is asked these types of q's BECAUSE he knows the math. If you take his .191489 (which is correct for hitting the flush in one hand) and subtract that from 1 you get .808511 as the probability you DON'T get a flush. .808511 to the 10th power is the probability you don't get the flush in all 10 hands. that's .11936 and 1/.11936 is 8.378, meaning you have one chance in that to get zero hits, which is what Bob said. 

That's the same answer I would have gotten using my crude approach but not rounding the numbers. That's what I wanted to know. It wasn't obvious in Bob's text. You want to calculate the probability of an event happening X consecutive times, you multiply the probability of it happening once by X. Thank you for your clarification.

Dancers program calculate one deck of cards servicing ten lines of outcome.  He should have calculated ten decks of cards which would have provided just one outcome instead of the eleven he posted. Multiline VP uses a different deck for each line as required by GC rules but even if one deck was redealt ten times Dancers numbers would still be incorrect.

The technique I showed does use 10 separate trials --- which can be used to calculate 10 separate decks --- where each deck has a 8/47 (or 9/47) chance of getting a positive result. The results show the chances of 0 flushes over the 10 decks, 1 flush, 2 flushes, etc.

If I were assuming one deck, the chances of getting 10 flushes would have to be zero --- given there are only 9 possible flush cards remaining in the deck. For the numbers shown, there is a small chance (very small) for 10-out-of-10 to occur.

Your comments on chaos theory are off base here as well. There is a MUCH higher chance of getting 0 hits than there are of getting 10 hits in these examples.

I certainly don't wish to argue with you, but if you pass my column by math professors they will tell you that my approach is appropriate.

Of curse they will Bob, but they also will say it is not truly accurate as you are not considering all probabilities or as some math experts will say "attractors". Chaos theory is not off base, it is a real factor involved in all probabilities and especially for all advantage players in order to gain an edge.  You base all of your calculations upon a deck of cards but the chaos factor in all VP machines is the RNG. 

Chaos theory is a branch of mathematics also canned non-linear Dynamics and has nothing to do with discrete probability. It describes systems that are deterministic but can appear random in certain situations, such as the 3-body problem.

..has as much applicability to calculating VP odds/probabilities as the phase of the moon or the signs of the zodiac. (or waving your hands in front of the machine before pushing the button for that matter - i.e. none)  I would be highly confident in the accuracy of Mr. Dancer's numbers.